Leverage diagnostic

As the validation set is used to test the model under real circumstances , it may occur that one or several samples are different from the calibration samples. When we use experimental designs to set the working space, this is not frequent, but it may well happen in quality control of raw materials in production, environmental samples, etc. Therefore, it is advisable to apply the Hotelling s T or the leverage diagnostics to the validation set. This would prevent wrong predictions from biasing the RMSEP and, therefore, the final decision on the acceptance of the PLS model. 

Outliers may heavily influence the result of PCA. Diagnostic plots help to find outliers (leverage points and orthogonal outliers) falling outside the hyper-ellipsoid which defines the PCA model. Essential is the use of robust methods that are tolerant against deviations from multivariate normal distributions. 

Studentized Concentration Residual vs. Sample Leverage Plot (Sample Diagnostic) This diagnostic is u.sed to more closeh examine individual samples. The sample ie erage for the /th sample is computed by... 

Values Whereas the sample leverage is based on the score vector of a sample, the value is based on the residual spectrum. The values are a convenient screening diagnostic for identifj ing samples that need closer examination. 

Figure 4.24 Studentised residuals leverage plot to detect outlier samples on the calibration set (a) general rules displayed on a hypothetical case and (b) diagnostics for the data from the worked example (Figure 4.9, mean centred, four factors in the PLS model).

Note that the most commonly used diagnostics to flag leverage points have traditionally been the diagonal elements / of the hat matrix H = X(X7X) X f These are equivalent to the Mahalanobis distances M/Xx,) because of the monotone relation... 

In particular, the leverage matrix H, also called influence matrix, is an important tool in regression diagnostics, containing information on the independent variables on which the model is built. 

Data structure analysis is the examination of the raw data for hidden structure, outliers, or leverage observations. This is repeated during the exploratory modeling (and nonlinear mixed effects modeling) steps using case deletion diagnostics (20). This type of analysis is important since outliers or leverage observations may occur in a population PM data set. It is equally important for the reduction of the covariate vector. 

One way to identify important predictor variables in a multiple regression setting is to do all possible regressions and choose the model based on some criteria, usually the coefficient of determination, adjusted coefficient of determination, or Mallows Cp. With this approach, a few candidate models are identified and then further explored for residual analysis, collinearity diagnostics, leverage analysis, etc. While useful, this method is rarely seen in the literature and cannot be advocated because the method is a dummy-ing down of the modeling process—the method relies too much on blind usage of the computer to solve a problem that should be left up to the modeler to solve. 

Available space is insufficient to permit demonstrating the partial plots for the example. However, Table 9 lists the leverages and the four influence diagnostics associated with individual observations... 

Figure 10.28 Simulated impedance waveform consisting of a higher frequency cardiac component superimposed on a low-frequency respiratory component The dotted line is the calculated mean impedance (measured during two respiratory cycles). An implantable impedance sensor may be able to leverage all three signal components in order to provide useful diagnostic or...

The responsibility to ensure that the DoD health monitoring needs are achieved clearly lies within the DoD. Ideally, more diagnostics could be leveraged from HHS via the National Institutes of Health (NIH), the Centers for Disease Control and Prevention (CDC) and/or the... 

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